1/1 (automatic unless something is incorrect)

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1 Your name and Perm # Econ 234A John Hartman Test 1 February 4, 20 Instructions: You have 60 minutes to complete this test, unless you arrive late. Late arrival will lower the time available to you, and you must finish at the same time as all other students. Each question shows how many points it is worth. Show all work in order to receive credit. You will receive partial credit for incorrect solutions in some instances. Clearly circle your answer(s) or else you may not receive full credit for a complete and correct solution. Cheating will not be tolerated during any test. Any suspected cheating will be reported to the relevant authorities on this issue. You are allowed to use a nonprogrammable four-function or scientific calculator that is NOT a communication device. You are NOT allowed to have a calculator that stores formulas, buttons that automatically calculate IRR, NPV, or any other concept covered in this class. You are NOT allowed to have a calculator that has the ability to produce graphs. If you use a calculator that does not meet these requirements, you will be assumed to be cheating. Unless otherwise specified, you can assume the following: Negative internal rates of return are not possible All equivalent annual cost problems are in real dollars You must show all of your algebraic work when solving problems. You are allowed to turn in your test early if there are at least 5 minutes remaining. As a courtesy to your classmates, you will not be allowed to leave during the final 5 minutes of the test. Your test should have 4 problems, some with multiple parts. The maximum possible point total is 34 points. If your test is incomplete, it is your responsibility to notify a proctor to get a new test. For your reference, an example of a well-labeled graph is below: Grading: Filling in name, perm #, & having photo ID 1/1 (automatic unless something is incorrect) Problems /33

2 For the following problems, you will need to write out the solution. You must show all work to receive credit. Each problem (or part of problem) shows the maximum point value. Provide at least four significant digits to each answer or you may not receive full credit for a correct solution. 1. (10 points) Suppose that you are advising a couple just about to get married about how much they need to save for retirement. The couple will retire in 40 years. The amount they will need to withdraw 40 years from today will be $1,000,000. Each subsequent year for the next 30 years the amount that they will withdraw will increase by 10% each year. (Note that the last withdrawal will occur 70 years from today.) When you ask the couple how they plan to save for their retirement, they tell you that they want to make 30 equal deposits of $X each year, starting five years from now. The total of these payments will be exactly enough to cover all of their retirement expenses. Find X if the effective annual interest rate is 12%. (Note: You can use the next page to solve this problem also.) PV of the total amount withdrawn = 1 (1.12) $1m = $.25756m 1 PV of the total amount deposited = (1.12) $X Solving for X, X = m = 50, = $.25756m

3 2. (7 points) Paula is planning the finances for a gold mine she has just purchased. She will pay $2,100,000 today to buy the land, gold rights, and equipment. She expects to extract gold worth $7,000,000 one year from today. Two years from today, she will sell her equipment for $500,000, and pay $5,000,000 to satisfy environmental regulations. If her assumptions are correct, find all annual internal rates of return, showing all of your algebra in the solution process. (Assume no other costs or benefits other than what is listed above.) $2.1m + $7m 1+ IRR $4.5m 1+ IRR ( ) 2 = 0. Rearranging the equation, then 2.1( 1+ IRR) 2 7( 1+ IRR) = 0. Denote x = 1+ IRR, with x > 1, then 2.1x 2 7x = 0. x = 7 ± = or (omit, since <1). Therefore, the legit IRR is IRR = %.

4 3. A 20-year bond with a face value of $8,000 was first issued five years ago. It pays annual coupons of 8% of its face value once per year, with the last coupon payment on the date the bond matures. The bond currently sells for $7,000. Assume that the next coupon payment will occur one year from today. (Note that the bond will mature in years.) (a) (3 points) Will the bond have a rate of return of more or less than 8%? Justify your answer completely in 40 words or less. The fact that bond price $7,000 is less than face value $8,000 indicates that the bond is sold at discount. It implies that the coupon interest is less than the ongoing rate of return of bond market. Therefore, the bond s rate of return (yield to maturity) is more than 8%. (b) (7 points) Narrow down the rate of return to a one percentage point span (e.g. 2-3%). Justify how you get your answer. (Hints: You may want to use the formula page sheet as scratch paper, but make sure you show your final work on this page. Also, you may want to think carefully on how to best solve this problem.) $7000 = $640 r Given r > 8%, r 1+ r ( ). Guess r = 9%,r.h.s = $ = $ ; ( 1.09) When r = 10%, r.h.s = $ = $ ( 1.1) Since bond price is a monotonically decreasing function of the discount rate, r (9%,10%).

5 4. (6 points) Bologna Sandwich Motors, Inc. expects to pay a $5 dividend four months from today. The company will pay a dividend on the same date each subsequent year. Each of the next four dividend payments will be 10% less than the previous payment. After that, the dividend will remain constant forever. Find the present value of this stock is assumed to be infinitely lived and the effective annual discount rate is 25%. PV = ( ) $5 $5 1 10% + + 1/3 (1.25) (1.25) 4/3 $5 ( 1 10% )2 + (1.25) 7/3 1 $5 1 10% (1.25) 10/3 = $ $ $ $ = $ ( ) 3 + $5 ( 1 10% )4.25